Question

What is a formula for the nth term of the given sequence? 36, -48, 64...

Answer 1

Answer:

A formula for the nth term of the given sequence is:

$a_n=36\left(-\frac{4}{3}\right)^{n-1}$

Step-by-step explanation:

Given the sequence

36, -48, 64...

We know that a geometric sequence has a constant ratio r and is defined by

$a_n=a_1\cdot r^{n-1}$

Compute the ratios of all the adjacent terms

$\frac{-48}{36}=-\frac{4}{3},\:\quad \frac{64}{-48}=-\frac{4}{3}$

The ratio of all the adjacent terms is the same and equal to

$r=-\frac{4}{3}$

Therefore, the given sequence is a geometric sequence.

As the first element of the sequence is

$a_1=36$

so substituting $a_1=36$ and $r=-\frac{4}{3}$ in the nth term

$a_n=a_1\cdot r^{n-1}$

$a_n=36\left(-\frac{4}{3}\right)^{n-1}$

Therefore, a formula for the nth term of the given sequence is:

$a_n=36\left(-\frac{4}{3}\right)^{n-1}$